【统计学】第四章

Evernote Export

一组数据的分布特征可以从那几个方面进行测度?

  • 数据的分布特征可以从三个方面进行测度和描述,一是分布的集中趋势,反映各数据向其中心值靠拢或聚集的程度;二是分布的离散程度,反映各数据远离其中心值的趋势;三是分布的形状,反映数据分布的偏态和峰态。

怎样理解平均数在统计学中的地位?

  • 平均数在统计学中具有重要的地位,它是进行统计分析和统计推断的基础。从统计思想上看,平均数是一组数据的重心所在,是数据误差相互抵消后的必然结果。
  • 比如,对同一事物进行多次测量,所得结果可能不一致,这是测量误差所致,也可能是其他因素的偶然影响,利用平均数作为其代表值,则可以使误差相互抵消,反映出事物必然性的数量特征。

简述四分位数的计算方法

  • 设下四分位数为QL,上四分位数为QU,根据四分位数的定义

QL=4n

QU=43n

如果位置是整数,四分位数就是该位置对应的值,如果是在0.5的位置上,则取该位置两侧值的平均数,如果在0.25或0.75的位置上,则四分位数等于该位置的下侧值加上按比例分摊位置两侧数值的差值。

对于比率数据的平均为什么采用几何平均?

  • 几何平均数是适用于特殊数据的一种平均数。它主要用于计算平均比率。当所掌握的变量值本身是比率的形式时,采用几何平均法计算平均比率更为合理。在实际应用中,几何平均数主要用于计算现象的平均增长率。

简述众数、中位数和平均数的特点和应用场合。

  • 众数是一组数据分布的峰值,不受极端值的影响。其缺点是具有不唯一性,一组数据可能有两个或多个众数,也可能没有众数。众数只有在数据量较多时才有意义,当数据量较少时,不宜使用众数。众数主要适合作为分类数据的集中趋势测度值。
  • 中位数是一组数据中间位置上的代表值,不受数据极端值的影响,当一组数据的分布偏斜程度较大时,使用中位数也许是一个好的选择。中位数主要适合作为顺序数据的集中趋势测度值。
  • 平均数是针对数值型数据计算的,而且利用了全部数据信息,它是实际中应用最广泛的集中趋势测度值。当数据呈对称分布或接近对称分布时,3个代表值相等或接近相等,这时则应选择平均数作为集中趋势的代表值。但是平均数的主要缺点是易受到数据极端值的影响,对于偏分布的数据,平均数的代表性差。因此,当数据为偏态分布,特别是偏斜程度较大时,可以考虑选择中位数或众数,这时它们的代表性比平均数好。

简述异众比率、四分位差、方差或标准差的应用场合。

  • 异众比率主要用于衡量众数对一组数据的代表程度。异众比率越大,说明非众数组的频数占总频数的比重越大,众数的代表性越差;异众比率越小,说明非众数组的频数占总频数的比重越小,众数的代表性越好。异众比率主要适合测度分类数据的离散程度,当然,对于顺序数据以及数值型数据也可以计算异众比率。
  • 四分位差反映了中间50%数据的离散程度,其数值越小,说明中间的数据越集中,其数值越大,说明中间的数据越分散。四分位差不受极值的影响。此外,由于中位数处于数据的中间位置,因此,四分位差的大小在一定程度上也说明了中位数对一组数据的代表程度。四分位差的大小在一定程度也说明了中位数对一组数据的代表程度。四分位差主要用于测度顺序数据的离散程度。对于数值型数据也可以计算四分位差,但是它不适合分类数据。
  • 方差是各变量值与其平均数离差平方的平均数。方差(或标准差)能较好的反应出数据的离散程度,是实际中应用最广的离散程度测度值。

标准分数有哪些用途?

  • 标准分数给出了一组数据中各数值的相对位置。

为什么要计算离散系数?

  • 离散系数也称为变异系数,它是一组数据的标准差与其相应的平均数之比。离散系数是测度数据离散程度的相对统计量,主要是用于比较不同样本数据的离散程度。离散系数越大,说明数据的离散程度也大,离散系数越小,说明数据的离散程度也越小。

测度数据分布形状的统计量有哪些?

  • 偏态系数
  • 峰态系数
  • 1.四分位差是上四分位数减下四分位数的结果
  • 2.各变量值与其平均数离差平方的平均数称为方差
  • 3.对于右偏分布,平均数、中位数、众数之间的关系是:平均数>中位数>众数
  • 4.在比较两组数据的离散程度时,不能直接比较它们的标准差,因为两组的数据计量单位不同
%23%23%23%20%E4%B8%80%E7%BB%84%E6%95%B0%E6%8D%AE%E7%9A%84%E5%88%86%E5%B8%83%E7%89%B9%E5%BE%81%E5%8F%AF%E4%BB%A5%E4%BB%8E%E9%82%A3%E5%87%A0%E4%B8%AA%E6%96%B9%E9%9D%A2%E8%BF%9B%E8%A1%8C%E6%B5%8B%E5%BA%A6%EF%BC%9F%0A%3E*%20%E6%95%B0%E6%8D%AE%E7%9A%84%E5%88%86%E5%B8%83%E7%89%B9%E5%BE%81%E5%8F%AF%E4%BB%A5%E4%BB%8E%E4%B8%89%E4%B8%AA%E6%96%B9%E9%9D%A2%E8%BF%9B%E8%A1%8C%E6%B5%8B%E5%BA%A6%E5%92%8C%E6%8F%8F%E8%BF%B0%EF%BC%8C%E4%B8%80%E6%98%AF%E5%88%86%E5%B8%83%E7%9A%84%E9%9B%86%E4%B8%AD%E8%B6%8B%E5%8A%BF%EF%BC%8C%E5%8F%8D%E6%98%A0%E5%90%84%E6%95%B0%E6%8D%AE%E5%90%91%E5%85%B6%E4%B8%AD%E5%BF%83%E5%80%BC%E9%9D%A0%E6%8B%A2%E6%88%96%E8%81%9A%E9%9B%86%E7%9A%84%E7%A8%8B%E5%BA%A6%EF%BC%9B%E4%BA%8C%E6%98%AF%E5%88%86%E5%B8%83%E7%9A%84%E7%A6%BB%E6%95%A3%E7%A8%8B%E5%BA%A6%EF%BC%8C%E5%8F%8D%E6%98%A0%E5%90%84%E6%95%B0%E6%8D%AE%E8%BF%9C%E7%A6%BB%E5%85%B6%E4%B8%AD%E5%BF%83%E5%80%BC%E7%9A%84%E8%B6%8B%E5%8A%BF%EF%BC%9B%E4%B8%89%E6%98%AF%E5%88%86%E5%B8%83%E7%9A%84%E5%BD%A2%E7%8A%B6%EF%BC%8C%E5%8F%8D%E6%98%A0%E6%95%B0%E6%8D%AE%E5%88%86%E5%B8%83%E7%9A%84%E5%81%8F%E6%80%81%E5%92%8C%E5%B3%B0%E6%80%81%E3%80%82%0A%0A%23%23%23%20%E6%80%8E%E6%A0%B7%E7%90%86%E8%A7%A3%E5%B9%B3%E5%9D%87%E6%95%B0%E5%9C%A8%E7%BB%9F%E8%AE%A1%E5%AD%A6%E4%B8%AD%E7%9A%84%E5%9C%B0%E4%BD%8D%EF%BC%9F%0A%3E*%20%E5%B9%B3%E5%9D%87%E6%95%B0%E5%9C%A8%E7%BB%9F%E8%AE%A1%E5%AD%A6%E4%B8%AD%E5%85%B7%E6%9C%89%E9%87%8D%E8%A6%81%E7%9A%84%E5%9C%B0%E4%BD%8D%EF%BC%8C%E5%AE%83%E6%98%AF%E8%BF%9B%E8%A1%8C%E7%BB%9F%E8%AE%A1%E5%88%86%E6%9E%90%E5%92%8C%E7%BB%9F%E8%AE%A1%E6%8E%A8%E6%96%AD%E7%9A%84%E5%9F%BA%E7%A1%80%E3%80%82%E4%BB%8E%E7%BB%9F%E8%AE%A1%E6%80%9D%E6%83%B3%E4%B8%8A%E7%9C%8B%EF%BC%8C%E5%B9%B3%E5%9D%87%E6%95%B0%E6%98%AF%E4%B8%80%E7%BB%84%E6%95%B0%E6%8D%AE%E7%9A%84%E9%87%8D%E5%BF%83%E6%89%80%E5%9C%A8%EF%BC%8C%E6%98%AF%E6%95%B0%E6%8D%AE%E8%AF%AF%E5%B7%AE%E7%9B%B8%E4%BA%92%E6%8A%B5%E6%B6%88%E5%90%8E%E7%9A%84%E5%BF%85%E7%84%B6%E7%BB%93%E6%9E%9C%E3%80%82%0A%3E*%20%E6%AF%94%E5%A6%82%EF%BC%8C%E5%AF%B9%E5%90%8C%E4%B8%80%E4%BA%8B%E7%89%A9%E8%BF%9B%E8%A1%8C%E5%A4%9A%E6%AC%A1%E6%B5%8B%E9%87%8F%EF%BC%8C%E6%89%80%E5%BE%97%E7%BB%93%E6%9E%9C%E5%8F%AF%E8%83%BD%E4%B8%8D%E4%B8%80%E8%87%B4%EF%BC%8C%E8%BF%99%E6%98%AF%E6%B5%8B%E9%87%8F%E8%AF%AF%E5%B7%AE%E6%89%80%E8%87%B4%EF%BC%8C%E4%B9%9F%E5%8F%AF%E8%83%BD%E6%98%AF%E5%85%B6%E4%BB%96%E5%9B%A0%E7%B4%A0%E7%9A%84%E5%81%B6%E7%84%B6%E5%BD%B1%E5%93%8D%EF%BC%8C%E5%88%A9%E7%94%A8%E5%B9%B3%E5%9D%87%E6%95%B0%E4%BD%9C%E4%B8%BA%E5%85%B6%E4%BB%A3%E8%A1%A8%E5%80%BC%EF%BC%8C%E5%88%99%E5%8F%AF%E4%BB%A5%E4%BD%BF%E8%AF%AF%E5%B7%AE%E7%9B%B8%E4%BA%92%E6%8A%B5%E6%B6%88%EF%BC%8C%E5%8F%8D%E6%98%A0%E5%87%BA%E4%BA%8B%E7%89%A9%E5%BF%85%E7%84%B6%E6%80%A7%E7%9A%84%E6%95%B0%E9%87%8F%E7%89%B9%E5%BE%81%E3%80%82%0A%0A%23%23%23%20%E7%AE%80%E8%BF%B0%E5%9B%9B%E5%88%86%E4%BD%8D%E6%95%B0%E7%9A%84%E8%AE%A1%E7%AE%97%E6%96%B9%E6%B3%95%0A%3E*%20%E8%AE%BE%E4%B8%8B%E5%9B%9B%E5%88%86%E4%BD%8D%E6%95%B0%E4%B8%BA%24Q_L%24%2C%E4%B8%8A%E5%9B%9B%E5%88%86%E4%BD%8D%E6%95%B0%E4%B8%BA%24Q_U%24%2C%E6%A0%B9%E6%8D%AE%E5%9B%9B%E5%88%86%E4%BD%8D%E6%95%B0%E7%9A%84%E5%AE%9A%E4%B9%89%0A%3E%20%24%24Q_L%20%3D%20%5Cfrac%7Bn%7D%7B4%7D%24%24%0A%3E%20%24%24Q_U%20%3D%20%5Cfrac%7B3n%7D%7B4%7D%24%24%0A%3E%20%E5%A6%82%E6%9E%9C%E4%BD%8D%E7%BD%AE%E6%98%AF%E6%95%B4%E6%95%B0%EF%BC%8C%E5%9B%9B%E5%88%86%E4%BD%8D%E6%95%B0%E5%B0%B1%E6%98%AF%E8%AF%A5%E4%BD%8D%E7%BD%AE%E5%AF%B9%E5%BA%94%E7%9A%84%E5%80%BC%EF%BC%8C%E5%A6%82%E6%9E%9C%E6%98%AF%E5%9C%A80.5%E7%9A%84%E4%BD%8D%E7%BD%AE%E4%B8%8A%EF%BC%8C%E5%88%99%E5%8F%96%E8%AF%A5%E4%BD%8D%E7%BD%AE%E4%B8%A4%E4%BE%A7%E5%80%BC%E7%9A%84%E5%B9%B3%E5%9D%87%E6%95%B0%EF%BC%8C%E5%A6%82%E6%9E%9C%E5%9C%A80.25%E6%88%960.75%E7%9A%84%E4%BD%8D%E7%BD%AE%E4%B8%8A%EF%BC%8C%E5%88%99%E5%9B%9B%E5%88%86%E4%BD%8D%E6%95%B0%E7%AD%89%E4%BA%8E%E8%AF%A5%E4%BD%8D%E7%BD%AE%E7%9A%84%E4%B8%8B%E4%BE%A7%E5%80%BC%E5%8A%A0%E4%B8%8A%E6%8C%89%E6%AF%94%E4%BE%8B%E5%88%86%E6%91%8A%E4%BD%8D%E7%BD%AE%E4%B8%A4%E4%BE%A7%E6%95%B0%E5%80%BC%E7%9A%84%E5%B7%AE%E5%80%BC%E3%80%82%0A%0A%23%23%23%20%E5%AF%B9%E4%BA%8E%E6%AF%94%E7%8E%87%E6%95%B0%E6%8D%AE%E7%9A%84%E5%B9%B3%E5%9D%87%E4%B8%BA%E4%BB%80%E4%B9%88%E9%87%87%E7%94%A8%E5%87%A0%E4%BD%95%E5%B9%B3%E5%9D%87%EF%BC%9F%0A%3E*%20%E5%87%A0%E4%BD%95%E5%B9%B3%E5%9D%87%E6%95%B0%E6%98%AF%E9%80%82%E7%94%A8%E4%BA%8E%E7%89%B9%E6%AE%8A%E6%95%B0%E6%8D%AE%E7%9A%84%E4%B8%80%E7%A7%8D%E5%B9%B3%E5%9D%87%E6%95%B0%E3%80%82%E5%AE%83%E4%B8%BB%E8%A6%81%E7%94%A8%E4%BA%8E%E8%AE%A1%E7%AE%97%E5%B9%B3%E5%9D%87%E6%AF%94%E7%8E%87%E3%80%82%E5%BD%93%E6%89%80%E6%8E%8C%E6%8F%A1%E7%9A%84%E5%8F%98%E9%87%8F%E5%80%BC%E6%9C%AC%E8%BA%AB%E6%98%AF%E6%AF%94%E7%8E%87%E7%9A%84%E5%BD%A2%E5%BC%8F%E6%97%B6%EF%BC%8C%E9%87%87%E7%94%A8%E5%87%A0%E4%BD%95%E5%B9%B3%E5%9D%87%E6%B3%95%E8%AE%A1%E7%AE%97%E5%B9%B3%E5%9D%87%E6%AF%94%E7%8E%87%E6%9B%B4%E4%B8%BA%E5%90%88%E7%90%86%E3%80%82%E5%9C%A8%E5%AE%9E%E9%99%85%E5%BA%94%E7%94%A8%E4%B8%AD%EF%BC%8C%E5%87%A0%E4%BD%95%E5%B9%B3%E5%9D%87%E6%95%B0%E4%B8%BB%E8%A6%81%E7%94%A8%E4%BA%8E%E8%AE%A1%E7%AE%97%E7%8E%B0%E8%B1%A1%E7%9A%84%E5%B9%B3%E5%9D%87%E5%A2%9E%E9%95%BF%E7%8E%87%E3%80%82%0A%0A%23%23%23%20%E7%AE%80%E8%BF%B0%E4%BC%97%E6%95%B0%E3%80%81%E4%B8%AD%E4%BD%8D%E6%95%B0%E5%92%8C%E5%B9%B3%E5%9D%87%E6%95%B0%E7%9A%84%E7%89%B9%E7%82%B9%E5%92%8C%E5%BA%94%E7%94%A8%E5%9C%BA%E5%90%88%E3%80%82%0A%3E*%20%E4%BC%97%E6%95%B0%E6%98%AF%E4%B8%80%E7%BB%84%E6%95%B0%E6%8D%AE%E5%88%86%E5%B8%83%E7%9A%84%E5%B3%B0%E5%80%BC%EF%BC%8C%E4%B8%8D%E5%8F%97%E6%9E%81%E7%AB%AF%E5%80%BC%E7%9A%84%E5%BD%B1%E5%93%8D%E3%80%82%E5%85%B6%E7%BC%BA%E7%82%B9%E6%98%AF%E5%85%B7%E6%9C%89%E4%B8%8D%E5%94%AF%E4%B8%80%E6%80%A7%EF%BC%8C%E4%B8%80%E7%BB%84%E6%95%B0%E6%8D%AE%E5%8F%AF%E8%83%BD%E6%9C%89%E4%B8%A4%E4%B8%AA%E6%88%96%E5%A4%9A%E4%B8%AA%E4%BC%97%E6%95%B0%EF%BC%8C%E4%B9%9F%E5%8F%AF%E8%83%BD%E6%B2%A1%E6%9C%89%E4%BC%97%E6%95%B0%E3%80%82%E4%BC%97%E6%95%B0%E5%8F%AA%E6%9C%89%E5%9C%A8%E6%95%B0%E6%8D%AE%E9%87%8F%E8%BE%83%E5%A4%9A%E6%97%B6%E6%89%8D%E6%9C%89%E6%84%8F%E4%B9%89%EF%BC%8C%E5%BD%93%E6%95%B0%E6%8D%AE%E9%87%8F%E8%BE%83%E5%B0%91%E6%97%B6%EF%BC%8C%E4%B8%8D%E5%AE%9C%E4%BD%BF%E7%94%A8%E4%BC%97%E6%95%B0%E3%80%82%E4%BC%97%E6%95%B0%E4%B8%BB%E8%A6%81%E9%80%82%E5%90%88%E4%BD%9C%E4%B8%BA%E5%88%86%E7%B1%BB%E6%95%B0%E6%8D%AE%E7%9A%84%E9%9B%86%E4%B8%AD%E8%B6%8B%E5%8A%BF%E6%B5%8B%E5%BA%A6%E5%80%BC%E3%80%82%0A%3E*%20%E4%B8%AD%E4%BD%8D%E6%95%B0%E6%98%AF%E4%B8%80%E7%BB%84%E6%95%B0%E6%8D%AE%E4%B8%AD%E9%97%B4%E4%BD%8D%E7%BD%AE%E4%B8%8A%E7%9A%84%E4%BB%A3%E8%A1%A8%E5%80%BC%EF%BC%8C%E4%B8%8D%E5%8F%97%E6%95%B0%E6%8D%AE%E6%9E%81%E7%AB%AF%E5%80%BC%E7%9A%84%E5%BD%B1%E5%93%8D%EF%BC%8C%E5%BD%93%E4%B8%80%E7%BB%84%E6%95%B0%E6%8D%AE%E7%9A%84%E5%88%86%E5%B8%83%E5%81%8F%E6%96%9C%E7%A8%8B%E5%BA%A6%E8%BE%83%E5%A4%A7%E6%97%B6%EF%BC%8C%E4%BD%BF%E7%94%A8%E4%B8%AD%E4%BD%8D%E6%95%B0%E4%B9%9F%E8%AE%B8%E6%98%AF%E4%B8%80%E4%B8%AA%E5%A5%BD%E7%9A%84%E9%80%89%E6%8B%A9%E3%80%82%E4%B8%AD%E4%BD%8D%E6%95%B0%E4%B8%BB%E8%A6%81%E9%80%82%E5%90%88%E4%BD%9C%E4%B8%BA%E9%A1%BA%E5%BA%8F%E6%95%B0%E6%8D%AE%E7%9A%84%E9%9B%86%E4%B8%AD%E8%B6%8B%E5%8A%BF%E6%B5%8B%E5%BA%A6%E5%80%BC%E3%80%82%0A%3E*%20%E5%B9%B3%E5%9D%87%E6%95%B0%E6%98%AF%E9%92%88%E5%AF%B9%E6%95%B0%E5%80%BC%E5%9E%8B%E6%95%B0%E6%8D%AE%E8%AE%A1%E7%AE%97%E7%9A%84%EF%BC%8C%E8%80%8C%E4%B8%94%E5%88%A9%E7%94%A8%E4%BA%86%E5%85%A8%E9%83%A8%E6%95%B0%E6%8D%AE%E4%BF%A1%E6%81%AF%EF%BC%8C%E5%AE%83%E6%98%AF%E5%AE%9E%E9%99%85%E4%B8%AD%E5%BA%94%E7%94%A8%E6%9C%80%E5%B9%BF%E6%B3%9B%E7%9A%84%E9%9B%86%E4%B8%AD%E8%B6%8B%E5%8A%BF%E6%B5%8B%E5%BA%A6%E5%80%BC%E3%80%82%E5%BD%93%E6%95%B0%E6%8D%AE%E5%91%88%E5%AF%B9%E7%A7%B0%E5%88%86%E5%B8%83%E6%88%96%E6%8E%A5%E8%BF%91%E5%AF%B9%E7%A7%B0%E5%88%86%E5%B8%83%E6%97%B6%EF%BC%8C3%E4%B8%AA%E4%BB%A3%E8%A1%A8%E5%80%BC%E7%9B%B8%E7%AD%89%E6%88%96%E6%8E%A5%E8%BF%91%E7%9B%B8%E7%AD%89%EF%BC%8C%E8%BF%99%E6%97%B6%E5%88%99%E5%BA%94%E9%80%89%E6%8B%A9%E5%B9%B3%E5%9D%87%E6%95%B0%E4%BD%9C%E4%B8%BA%E9%9B%86%E4%B8%AD%E8%B6%8B%E5%8A%BF%E7%9A%84%E4%BB%A3%E8%A1%A8%E5%80%BC%E3%80%82%E4%BD%86%E6%98%AF%E5%B9%B3%E5%9D%87%E6%95%B0%E7%9A%84%E4%B8%BB%E8%A6%81%E7%BC%BA%E7%82%B9%E6%98%AF%E6%98%93%E5%8F%97%E5%88%B0%E6%95%B0%E6%8D%AE%E6%9E%81%E7%AB%AF%E5%80%BC%E7%9A%84%E5%BD%B1%E5%93%8D%EF%BC%8C%E5%AF%B9%E4%BA%8E%E5%81%8F%E5%88%86%E5%B8%83%E7%9A%84%E6%95%B0%E6%8D%AE%EF%BC%8C%E5%B9%B3%E5%9D%87%E6%95%B0%E7%9A%84%E4%BB%A3%E8%A1%A8%E6%80%A7%E5%B7%AE%E3%80%82%E5%9B%A0%E6%AD%A4%EF%BC%8C%E5%BD%93%E6%95%B0%E6%8D%AE%E4%B8%BA%E5%81%8F%E6%80%81%E5%88%86%E5%B8%83%EF%BC%8C%E7%89%B9%E5%88%AB%E6%98%AF%E5%81%8F%E6%96%9C%E7%A8%8B%E5%BA%A6%E8%BE%83%E5%A4%A7%E6%97%B6%EF%BC%8C%E5%8F%AF%E4%BB%A5%E8%80%83%E8%99%91%E9%80%89%E6%8B%A9%E4%B8%AD%E4%BD%8D%E6%95%B0%E6%88%96%E4%BC%97%E6%95%B0%EF%BC%8C%E8%BF%99%E6%97%B6%E5%AE%83%E4%BB%AC%E7%9A%84%E4%BB%A3%E8%A1%A8%E6%80%A7%E6%AF%94%E5%B9%B3%E5%9D%87%E6%95%B0%E5%A5%BD%E3%80%82%0A%0A%23%23%23%20%E7%AE%80%E8%BF%B0%E5%BC%82%E4%BC%97%E6%AF%94%E7%8E%87%E3%80%81%E5%9B%9B%E5%88%86%E4%BD%8D%E5%B7%AE%E3%80%81%E6%96%B9%E5%B7%AE%E6%88%96%E6%A0%87%E5%87%86%E5%B7%AE%E7%9A%84%E5%BA%94%E7%94%A8%E5%9C%BA%E5%90%88%E3%80%82%0A%3E*%20%E5%BC%82%E4%BC%97%E6%AF%94%E7%8E%87%E4%B8%BB%E8%A6%81%E7%94%A8%E4%BA%8E%E8%A1%A1%E9%87%8F%E4%BC%97%E6%95%B0%E5%AF%B9%E4%B8%80%E7%BB%84%E6%95%B0%E6%8D%AE%E7%9A%84%E4%BB%A3%E8%A1%A8%E7%A8%8B%E5%BA%A6%E3%80%82%E5%BC%82%E4%BC%97%E6%AF%94%E7%8E%87%E8%B6%8A%E5%A4%A7%EF%BC%8C%E8%AF%B4%E6%98%8E%E9%9D%9E%E4%BC%97%E6%95%B0%E7%BB%84%E7%9A%84%E9%A2%91%E6%95%B0%E5%8D%A0%E6%80%BB%E9%A2%91%E6%95%B0%E7%9A%84%E6%AF%94%E9%87%8D%E8%B6%8A%E5%A4%A7%EF%BC%8C%E4%BC%97%E6%95%B0%E7%9A%84%E4%BB%A3%E8%A1%A8%E6%80%A7%E8%B6%8A%E5%B7%AE%EF%BC%9B%E5%BC%82%E4%BC%97%E6%AF%94%E7%8E%87%E8%B6%8A%E5%B0%8F%EF%BC%8C%E8%AF%B4%E6%98%8E%E9%9D%9E%E4%BC%97%E6%95%B0%E7%BB%84%E7%9A%84%E9%A2%91%E6%95%B0%E5%8D%A0%E6%80%BB%E9%A2%91%E6%95%B0%E7%9A%84%E6%AF%94%E9%87%8D%E8%B6%8A%E5%B0%8F%EF%BC%8C%E4%BC%97%E6%95%B0%E7%9A%84%E4%BB%A3%E8%A1%A8%E6%80%A7%E8%B6%8A%E5%A5%BD%E3%80%82%E5%BC%82%E4%BC%97%E6%AF%94%E7%8E%87%E4%B8%BB%E8%A6%81%E9%80%82%E5%90%88%E6%B5%8B%E5%BA%A6%E5%88%86%E7%B1%BB%E6%95%B0%E6%8D%AE%E7%9A%84%E7%A6%BB%E6%95%A3%E7%A8%8B%E5%BA%A6%EF%BC%8C%E5%BD%93%E7%84%B6%EF%BC%8C%E5%AF%B9%E4%BA%8E%E9%A1%BA%E5%BA%8F%E6%95%B0%E6%8D%AE%E4%BB%A5%E5%8F%8A%E6%95%B0%E5%80%BC%E5%9E%8B%E6%95%B0%E6%8D%AE%E4%B9%9F%E5%8F%AF%E4%BB%A5%E8%AE%A1%E7%AE%97%E5%BC%82%E4%BC%97%E6%AF%94%E7%8E%87%E3%80%82%0A%3E*%20%E5%9B%9B%E5%88%86%E4%BD%8D%E5%B7%AE%E5%8F%8D%E6%98%A0%E4%BA%86%E4%B8%AD%E9%97%B450%25%E6%95%B0%E6%8D%AE%E7%9A%84%E7%A6%BB%E6%95%A3%E7%A8%8B%E5%BA%A6%EF%BC%8C%E5%85%B6%E6%95%B0%E5%80%BC%E8%B6%8A%E5%B0%8F%EF%BC%8C%E8%AF%B4%E6%98%8E%E4%B8%AD%E9%97%B4%E7%9A%84%E6%95%B0%E6%8D%AE%E8%B6%8A%E9%9B%86%E4%B8%AD%EF%BC%8C%E5%85%B6%E6%95%B0%E5%80%BC%E8%B6%8A%E5%A4%A7%EF%BC%8C%E8%AF%B4%E6%98%8E%E4%B8%AD%E9%97%B4%E7%9A%84%E6%95%B0%E6%8D%AE%E8%B6%8A%E5%88%86%E6%95%A3%E3%80%82%E5%9B%9B%E5%88%86%E4%BD%8D%E5%B7%AE%E4%B8%8D%E5%8F%97%E6%9E%81%E5%80%BC%E7%9A%84%E5%BD%B1%E5%93%8D%E3%80%82%E6%AD%A4%E5%A4%96%EF%BC%8C%E7%94%B1%E4%BA%8E%E4%B8%AD%E4%BD%8D%E6%95%B0%E5%A4%84%E4%BA%8E%E6%95%B0%E6%8D%AE%E7%9A%84%E4%B8%AD%E9%97%B4%E4%BD%8D%E7%BD%AE%EF%BC%8C%E5%9B%A0%E6%AD%A4%EF%BC%8C%E5%9B%9B%E5%88%86%E4%BD%8D%E5%B7%AE%E7%9A%84%E5%A4%A7%E5%B0%8F%E5%9C%A8%E4%B8%80%E5%AE%9A%E7%A8%8B%E5%BA%A6%E4%B8%8A%E4%B9%9F%E8%AF%B4%E6%98%8E%E4%BA%86%E4%B8%AD%E4%BD%8D%E6%95%B0%E5%AF%B9%E4%B8%80%E7%BB%84%E6%95%B0%E6%8D%AE%E7%9A%84%E4%BB%A3%E8%A1%A8%E7%A8%8B%E5%BA%A6%E3%80%82%E5%9B%9B%E5%88%86%E4%BD%8D%E5%B7%AE%E7%9A%84%E5%A4%A7%E5%B0%8F%E5%9C%A8%E4%B8%80%E5%AE%9A%E7%A8%8B%E5%BA%A6%E4%B9%9F%E8%AF%B4%E6%98%8E%E4%BA%86%E4%B8%AD%E4%BD%8D%E6%95%B0%E5%AF%B9%E4%B8%80%E7%BB%84%E6%95%B0%E6%8D%AE%E7%9A%84%E4%BB%A3%E8%A1%A8%E7%A8%8B%E5%BA%A6%E3%80%82%E5%9B%9B%E5%88%86%E4%BD%8D%E5%B7%AE%E4%B8%BB%E8%A6%81%E7%94%A8%E4%BA%8E%E6%B5%8B%E5%BA%A6%E9%A1%BA%E5%BA%8F%E6%95%B0%E6%8D%AE%E7%9A%84%E7%A6%BB%E6%95%A3%E7%A8%8B%E5%BA%A6%E3%80%82%E5%AF%B9%E4%BA%8E%E6%95%B0%E5%80%BC%E5%9E%8B%E6%95%B0%E6%8D%AE%E4%B9%9F%E5%8F%AF%E4%BB%A5%E8%AE%A1%E7%AE%97%E5%9B%9B%E5%88%86%E4%BD%8D%E5%B7%AE%EF%BC%8C%E4%BD%86%E6%98%AF%E5%AE%83%E4%B8%8D%E9%80%82%E5%90%88%E5%88%86%E7%B1%BB%E6%95%B0%E6%8D%AE%E3%80%82%0A%3E*%20%E6%96%B9%E5%B7%AE%E6%98%AF%E5%90%84%E5%8F%98%E9%87%8F%E5%80%BC%E4%B8%8E%E5%85%B6%E5%B9%B3%E5%9D%87%E6%95%B0%E7%A6%BB%E5%B7%AE%E5%B9%B3%E6%96%B9%E7%9A%84%E5%B9%B3%E5%9D%87%E6%95%B0%E3%80%82%E6%96%B9%E5%B7%AE(%E6%88%96%E6%A0%87%E5%87%86%E5%B7%AE)%E8%83%BD%E8%BE%83%E5%A5%BD%E7%9A%84%E5%8F%8D%E5%BA%94%E5%87%BA%E6%95%B0%E6%8D%AE%E7%9A%84%E7%A6%BB%E6%95%A3%E7%A8%8B%E5%BA%A6%EF%BC%8C%E6%98%AF%E5%AE%9E%E9%99%85%E4%B8%AD%E5%BA%94%E7%94%A8%E6%9C%80%E5%B9%BF%E7%9A%84%E7%A6%BB%E6%95%A3%E7%A8%8B%E5%BA%A6%E6%B5%8B%E5%BA%A6%E5%80%BC%E3%80%82%0A%0A%23%23%23%20%E6%A0%87%E5%87%86%E5%88%86%E6%95%B0%E6%9C%89%E5%93%AA%E4%BA%9B%E7%94%A8%E9%80%94%EF%BC%9F%0A%3E*%20%E6%A0%87%E5%87%86%E5%88%86%E6%95%B0%E7%BB%99%E5%87%BA%E4%BA%86%E4%B8%80%E7%BB%84%E6%95%B0%E6%8D%AE%E4%B8%AD%E5%90%84%E6%95%B0%E5%80%BC%E7%9A%84%E7%9B%B8%E5%AF%B9%E4%BD%8D%E7%BD%AE%E3%80%82%0A%0A%23%23%23%20%E4%B8%BA%E4%BB%80%E4%B9%88%E8%A6%81%E8%AE%A1%E7%AE%97%E7%A6%BB%E6%95%A3%E7%B3%BB%E6%95%B0%EF%BC%9F%0A%3E*%20%E7%A6%BB%E6%95%A3%E7%B3%BB%E6%95%B0%E4%B9%9F%E7%A7%B0%E4%B8%BA%E5%8F%98%E5%BC%82%E7%B3%BB%E6%95%B0%EF%BC%8C%E5%AE%83%E6%98%AF%E4%B8%80%E7%BB%84%E6%95%B0%E6%8D%AE%E7%9A%84%E6%A0%87%E5%87%86%E5%B7%AE%E4%B8%8E%E5%85%B6%E7%9B%B8%E5%BA%94%E7%9A%84%E5%B9%B3%E5%9D%87%E6%95%B0%E4%B9%8B%E6%AF%94%E3%80%82%E7%A6%BB%E6%95%A3%E7%B3%BB%E6%95%B0%E6%98%AF%E6%B5%8B%E5%BA%A6%E6%95%B0%E6%8D%AE%E7%A6%BB%E6%95%A3%E7%A8%8B%E5%BA%A6%E7%9A%84%E7%9B%B8%E5%AF%B9%E7%BB%9F%E8%AE%A1%E9%87%8F%EF%BC%8C%E4%B8%BB%E8%A6%81%E6%98%AF%E7%94%A8%E4%BA%8E%E6%AF%94%E8%BE%83%E4%B8%8D%E5%90%8C%E6%A0%B7%E6%9C%AC%E6%95%B0%E6%8D%AE%E7%9A%84%E7%A6%BB%E6%95%A3%E7%A8%8B%E5%BA%A6%E3%80%82%E7%A6%BB%E6%95%A3%E7%B3%BB%E6%95%B0%E8%B6%8A%E5%A4%A7%EF%BC%8C%E8%AF%B4%E6%98%8E%E6%95%B0%E6%8D%AE%E7%9A%84%E7%A6%BB%E6%95%A3%E7%A8%8B%E5%BA%A6%E4%B9%9F%E5%A4%A7%EF%BC%8C%E7%A6%BB%E6%95%A3%E7%B3%BB%E6%95%B0%E8%B6%8A%E5%B0%8F%EF%BC%8C%E8%AF%B4%E6%98%8E%E6%95%B0%E6%8D%AE%E7%9A%84%E7%A6%BB%E6%95%A3%E7%A8%8B%E5%BA%A6%E4%B9%9F%E8%B6%8A%E5%B0%8F%E3%80%82%0A%0A%23%23%23%20%E6%B5%8B%E5%BA%A6%E6%95%B0%E6%8D%AE%E5%88%86%E5%B8%83%E5%BD%A2%E7%8A%B6%E7%9A%84%E7%BB%9F%E8%AE%A1%E9%87%8F%E6%9C%89%E5%93%AA%E4%BA%9B%EF%BC%9F%0A%3E*%20%E5%81%8F%E6%80%81%E7%B3%BB%E6%95%B0%0A%3E*%20%E5%B3%B0%E6%80%81%E7%B3%BB%E6%95%B0%0A%0A%0A*%201.%E5%9B%9B%E5%88%86%E4%BD%8D%E5%B7%AE%E6%98%AF%E4%B8%8A%E5%9B%9B%E5%88%86%E4%BD%8D%E6%95%B0%E5%87%8F%E4%B8%8B%E5%9B%9B%E5%88%86%E4%BD%8D%E6%95%B0%E7%9A%84%E7%BB%93%E6%9E%9C%0A*%202.%E5%90%84%E5%8F%98%E9%87%8F%E5%80%BC%E4%B8%8E%E5%85%B6%E5%B9%B3%E5%9D%87%E6%95%B0%E7%A6%BB%E5%B7%AE%E5%B9%B3%E6%96%B9%E7%9A%84%E5%B9%B3%E5%9D%87%E6%95%B0%E7%A7%B0%E4%B8%BA%E6%96%B9%E5%B7%AE%0A*%203.%E5%AF%B9%E4%BA%8E%E5%8F%B3%E5%81%8F%E5%88%86%E5%B8%83%EF%BC%8C%E5%B9%B3%E5%9D%87%E6%95%B0%E3%80%81%E4%B8%AD%E4%BD%8D%E6%95%B0%E3%80%81%E4%BC%97%E6%95%B0%E4%B9%8B%E9%97%B4%E7%9A%84%E5%85%B3%E7%B3%BB%E6%98%AF%EF%BC%9A**%E5%B9%B3%E5%9D%87%E6%95%B0%3E%E4%B8%AD%E4%BD%8D%E6%95%B0%3E%E4%BC%97%E6%95%B0**%0A*%204.%E5%9C%A8%E6%AF%94%E8%BE%83%E4%B8%A4%E7%BB%84%E6%95%B0%E6%8D%AE%E7%9A%84%E7%A6%BB%E6%95%A3%E7%A8%8B%E5%BA%A6%E6%97%B6%EF%BC%8C%E4%B8%8D%E8%83%BD%E7%9B%B4%E6%8E%A5%E6%AF%94%E8%BE%83%E5%AE%83%E4%BB%AC%E7%9A%84%E6%A0%87%E5%87%86%E5%B7%AE%EF%BC%8C%E5%9B%A0%E4%B8%BA%E4%B8%A4%E7%BB%84%E7%9A%84%E6%95%B0%E6%8D%AE**%E8%AE%A1%E9%87%8F%E5%8D%95%E4%BD%8D%E4%B8%8D%E5%90%8C**

转载于:https://www.cnblogs.com/pandaboy1123/p/10449128.html

你可能感兴趣的:(【统计学】第四章)